Question

Two of the most expensive cars in the world are car A and car B. The prices of these two cars differ by more than ​$10,000. The price of car A is ​$130,645. a. Assuming that you do not know which model is more​ expensive, write an absolute value inequality that describes this situation. Use x for the price of car B. b. What are the possibilities for the price of car​ B?

Answer 1

Part a.

x = price of car B

x-130645 = difference in price from car A to car B

If x is the larger price, then x-130645 will be positive. If x is the smaller price, then x-130645 is negative.

In short,

• x-130645 > 0 when x > 130645
• x-130645 < 0 when x < 130645

Using absolute value will give us

|x-130645| = positive difference in price

The result of an absolute value is never negative

We write the |x-130645| > 10000 to indicate that the difference in price is more than 10000 dollars.

-----------

Answer:  | x-130645 | > 10000

================================================

Part b.

We'll use the idea that if |x| > k, then x < -k or x > k

to get the following

|x-130645| > 10000

x-130645 < -10000 or x-130645 > 10000

x < -10000+130645  or  x > 10000+130645

x < 120645  or  x > 140645

-----------

Answer:

Car B has a price less than $120,645

OR

Car B has a price greater than $140,645

So basically anything that is not between 120645 and 140645. The price has to be positive of course.

Answer 2

Answer:

| x-130645 | > 10000